the radius of a curvature is 10ft and the height of the segment is 2ft. What is the length of the chord
Let the length of the chord be x.
Draw a perpendicular bisector to the chord and let it intersect the circles at A and B. The mid-point of the chord is M.
Since the radius is 10 ft, the diameter is 20 ft. mAM=2 ft, and mMB = 20-2=18 ft.
By the property of intersecting chords,
(x/2)² = mAM . mMB
=2*18
=36
x/2=6 ft
x= 12 ft.
To find the length of the chord, we can use the formula for the length of a chord in a segment of a circle:
Length of Chord = 2 * √(r^2 - h^2)
Where:
r is the radius of curvature
h is the height of the segment
Given that the radius of curvature is 10ft and the height of the segment is 2ft, we can substitute these values into the formula:
Length of Chord = 2 * √(10^2 - 2^2)
Length of Chord = 2 * √(100 - 4)
Length of Chord = 2 * √96
Length of Chord ≈ 2 * 9.797959...
Length of Chord ≈ 19.596 ft
Therefore, the length of the chord is approximately 19.596 feet.
To find the length of the chord in a segment of a circle, you'll need to use the formula for the length of a chord in a circle segment. The formula is given by:
chord length = 2 * square root of (radius^2 - height * (2 * radius - height))
Let's plug in the given values into the formula:
radius = 10ft
height = 2ft
chord length = 2 * square root of (10^2 - 2 * (2 * 10 - 2))
= 2 * square root of (100 - 2 * (20 - 2))
= 2 * square root of (100 - 2 * 18)
= 2 * square root of (100 - 36)
= 2 * square root of (64)
= 2 * 8
= 16ft
Therefore, the length of the chord in the given segment is 16 feet.